Chapter 4.3, Problem 13GP

To determine

To find the product and express the result using positive exponents.

Answer to Problem 13GP

The product is , $\frac{{\text{r}}^8}{{\text{r}}^4}={\text{r}}^4$

Explanation of Solution

Given information: The expression is, $\frac{{\text{r}}^8}{{\text{r}}^4}$

Concept used: The products of powers property is defined by,

Multiply powers with the same base by adding their exponents.

  $a^m.a^n=a^{m+n}$

Calculation : The product of the numbers is obtained as,

  $\begin{array}{l}\frac{{\text{r}}^8}{{\text{r}}^4}={\text{r}}^8.{\text{r}}^{-4}\\ {\text{ = r}}^{8+\left(-4\right)}\left(\text{Product of the powers property; the common base is r }\right).\\ ={\text{r}}^4\left(\text{Add the exponents}\right).\end{array}$

Hence,the product is $\frac{{\text{r}}^8}{{\text{r}}^4}={\text{r}}^4$